Question

Rain is falling vertically with a speed of $30m/s.$ A man rides a bicycle with a speed of $10m/s$ from East to West direction. At what the angle with the vertical, he sees the rain falling?

• A. ${\tan }^{-1}\left(\frac{1}{3}\right)$ towards West
• B. ${\tan }^{-1}(3)$ towards West
• C. ${\tan }^{-1}\left(\frac{1}{3}\right)$ towards East
• D. ${\tan }^{-1}(3)$ towards East

Answer 1

Answer: (A)

Given, speed of rain in vertical direction,
$v_r=30m/s$
Speed of man, $v_m=10m/s$ from direction East to West

The given situation is shown in the above figure. If $\theta$ be the angle from vertical in south direction, then,
$\tan \theta =\frac{v_m}{v_r}=\frac{10}{30}=\frac{1}{3}$
$\therefore \theta ={\tan }^{-1}\left(\frac{1}{3}\right)$ towards West direction.